Abstract: The multidimensional modal theory is applied to solveliquid nonlinear sloshing in right circular cylindrical tank intranslatory motion. The general infinite dimensional modal system describingliquid nonlinear sloshing is derived first by pressure integral variationalprinciple. After selecting two dominating modes and three secondarymodes based on the Narimanov-Moiseev third order asymptotichypothesis, the infinite dimensional modal system is reduced to afive dimensional asymptotic modal system. The numericalintegrations of this modal system reveal some typical nonlinearcharacteristics, such as the amplitude difference between wave peak and wavetrough and the dispersion effect.